Costs and break-even analysis

Last time

Before we start: last time, in The role of marketing, markets and segmentation, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.

When does a business start to profit?

A new business sells its first products, but it is still losing money. At some point, if sales keep growing, it starts making a profit. That point is break-even. This lesson covers the types of cost, and how to find break-even by calculation and on a chart.

Fixed and variable costs

Fixed costs do not change with output: rent, insurance, salaries, and loan interest. They must be paid even if nothing is made. Variable costs change directly with output: raw materials, packaging, and piece-rate wages. Total cost is fixed costs plus variable costs.

Average cost

Average cost is total cost divided by output. A firm has fixed costs of 12,000 dollars and a variable cost of 6 dollars a unit. At 3,000 units, total cost is 12,000 plus 18,000, which is 30,000 dollars. Average cost is 30,000 divided by 3,000, which is 10 dollars. As output rises, fixed cost is spread wider, so average cost falls.

Contribution

Contribution per unit is the selling price minus the variable cost per unit. If the price is 10 dollars and the variable cost is 6, each unit contributes 4 dollars towards fixed costs. Once the fixed costs are covered, each extra contribution is profit.

The break-even calculation

Break-even output is the level of output where total revenue equals total cost: no profit and no loss. Break-even output equals fixed costs divided by contribution per unit. 12,000 dollars divided by 4 dollars is 3,000 units. Below 3,000, a loss; above it, a profit.

The break-even chart

Here the axes are output in thousands of units, and costs and revenue in thousands of dollars. Fixed cost is a flat line at 12. Total cost starts at 12 and rises by 6 a unit. Revenue starts at zero and rises by 10 a unit. They cross at 3 thousand units and 30 thousand dollars: the break-even point.

Margin of safety

The margin of safety is the amount by which actual output is above break-even output. If the firm sells 4,000 units, the margin of safety is 4,000 minus 3,000, which is 1,000 units. A bigger margin means sales could fall further before the firm makes a loss.

What changes break-even

A higher price raises contribution, so break-even output falls. Higher fixed costs, or higher variable costs, raise break-even output. So a business can test decisions: what if we raise the price, or move to cheaper premises?

Limits of break-even

It assumes every unit made is sold, which may not happen. It assumes the price and the variable cost per unit stay the same, though bulk buying and discounts change them. And fixed costs can change, such as a rent rise. So use it as a guide, not a certainty.

Mistakes that lose marks

Mistake one: dividing fixed costs by the price, not by the contribution. Mistake two: giving break-even in dollars when units are asked, or forgetting units. Mistake three: in a choose-a-product question, calculating but not using the numbers to decide. The fix: show the formula, the working, the units, and use the answer.

The full-marks tip

The full-marks tip: show the formula, the working and the units: fixed costs divided by contribution per unit. In a choice question, compare break-even and margin of safety for each option, then decide.

On one card

So, on one card: costs and break-even. Keep it for revision.